Unfolding of saddle-nodes and their Dulac time
Mardesic, Pavao (Université de Bourgogne. Institut de Mathématiques de Bourgogne)
Marín Pérez, David (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Saavedra, M. (Universidad de Concepción. Departamento de Matemáticas)
Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)

Date:	2016
Abstract:	In this paper we study unfoldings of saddle-nodes and their Dulac time. By unfolding a saddle-node, saddles and nodes appear. In the first result (Theorem A) we give a uniform asymptotic expansion of the trajectories arriving at the node. Uniformity is with respect to all parameters including the unfolding parameter bringing the node to a saddle-node and a parameter belonging to a space of functions. In the second part, we apply this first result for proving a regularity result (Theorem B) on the Dulac time (time of Dulac map) of an unfolding of a saddle-node. This result is a building block in the study of bifurcations of critical periods in a neighborhood of a polycycle. Finally, we apply Theorem A and Theorem B to the study of critical periods of the Loud family of quadratic centers and we prove that no bifurcation occurs for certain values of the parameters (Theorem C).
Grants:	Ministerio de Economía y Competitividad MTM2011-26674-C02-01 Ministerio de Economía y Competitividad MTM-2008-03437
Note:	Altres ajuts: UNAB10-4E-378, co-funded by ERDF "A way to build Europe" and by the French ANR-11-BS01-0009 STAAVF.
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Period function ; Unfolding of a saddle-node ; Asymptotic expansions
Published in:	Journal of differential equations, Vol. 261, issue 11 (Dec. 2016) , p. 6411-6436, ISSN 1090-2732

DOI: 10.1016/j.jde.2016.08.040

Post-print 21 p, 2.2 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
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